Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include "bits/stdc++.h"

#define REP(i,n) for(ll i=0;i<ll(n);++i)
#define RREP(i,n) for(ll i=ll(n)-1;i>=0;--i)
#define FOR(i,m,n) for(ll i=m;i<ll(n);++i)
#define RFOR(i,m,n) for(ll i=ll(n)-1;i>=ll(m);--i)
#define ALL(v) (v).begin(),(v).end()
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end());
#define INF 1000000001ll
#define MOD 1000000007ll
#define EPS 1e-9

constexpr int dx[8] = { 1,1,0,-1,-1,-1,0,1 };
constexpr int dy[8] = { 0,1,1,1,0,-1,-1,-1 };


using namespace std;

using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template <class T> bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; }
template <class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; }
struct Edge { int from; int to; long long weight; };
typedef std::vector<Edge> Edges;
typedef std::vector<Edges> Graph;
typedef std::pair<long long, int> P;

std::vector<long long> dijkstra(const Graph& g, int src) {
	std::vector<long long> d(g.size(), std::numeric_limits<long long>::max());
	d[src] = 0;
	//vector<int> prev(g.size());
	std::priority_queue<P, std::vector<P>, std::greater<P>> q;
	q.push({ 0, src });
	while (!q.empty()) {
		auto p = q.top(); q.pop();
		int v = p.second;
		if (p.first > d[v]) continue;
		for (int i = 0; i < (int)g[v].size(); ++i) {
			Edge e = g[v][i];
			if (d[e.to] > d[v] + e.weight) {
				d[e.to] = d[v] + e.weight;
				q.push({ d[e.to],e.to });
				//prev[e.to] = v;
			}
		}
	}
	return d;
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, m, s, t;
	cin >> n >> m >> s >> t;
	s--; t--;
	Graph g(n);
	REP(i, m) {
		int a, b; cin >> a >> b;
		a--; b--;
		g[a].push_back({ a,b,1 });
		g[b].push_back({ b,a,1 });
	}
	auto a = dijkstra(g, s), b = dijkstra(g, t);
	ll d = a[t];
	vl cnta(n), cntb(n);
	REP(i, n) {
		if (a[i] == numeric_limits<ll>::max())continue;
		cnta[a[i]]++;
		cntb[b[i]]++;
	}
	ll ans = 0;
	REP(i, d - 1) {
		ans += cnta[i] * cntb[d - i - 2];
	}
	cout << ans << endl;


}